Velocity Verlet-based optimization for variational quantum eigensolvers

Abstract

The Variational Quantum Eigensolver (VQE) is a key algorithm for near-term quantum computers, yet its performance is often limited by the classical optimization of circuit parameters. We propose using the velocity Verlet algorithm, inspired by classical molecular dynamics, to address this challenge. By introducing an inertial "velocity" term, our method efficiently explores complex energy landscapes. We compare its performance against standard optimizers on H${}_2$ and LiH molecules. For H${}_2$, our method achieves chemical accuracy with fewer quantum circuit evaluations than L-BFGS-B. For LiH, it attains the lowest final energy, demonstrating its potential for high-accuracy VQE simulations.

arXiv commentMain text: 7 pages, 4 figures, 2 tables

References in corpus (26)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• A variational eigenvalue solver on a quantum processor
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Barren plateaus in quantum neural network training landscapes
• The theory of variational hybrid quantum-classical algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum machine learning in feature Hilbert spaces
• Quantum Circuit Learning
• Quantum Chemistry in the Age of Quantum Computing
• Parameterized quantum circuits as machine learning models
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Evaluating analytic gradients on quantum hardware
• The Variational Quantum Eigensolver: a review of methods and best practices
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Variational ansatz-based quantum simulation of imaginary time evolution
• Hybrid quantum-classical algorithms and quantum error mitigation
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Quantum Natural Gradient
• Qulacs: a fast and versatile quantum circuit simulator for research purpose
• Subspace-search variational quantum eigensolver for excited states
• Universal Nonlinear Disordered Wave Packet Subdiffusion: 12 Decades
• Collective optimization for variational quantum eigensolvers
• Hamiltonian simulation-based quantum-selected configuration interaction for large-scale electronic structure calculations with a quantum computer
• Uniqueness and Optimality of Dynamical Extensions of Divergences
• Quantum-selected configuration interaction with time-evolved state